NucIear Physics A461 (1987) 33%. 34Oc North-Holland, Amsterdam 335c 1. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA AN EXACT FERMION ALGORITHM AND THE PSEUDO-FERMIONS* R. V. GAVAI Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA** A. GOCKSCH Physics Department, University of California at San Diego, La Jolla, CA 92093, USA Using an algorithm that incorporates the fermion determinant exactly, we investigated the full QCD with 4 light dynamical flavours on a small, 4", lattice. Comparing the results so obtained for various physical observables with those obtained by using the pseudo-fermion algorithm instead, we found a quantitatively good agreement. INTRODUCTION Numerical simulations of lattice gauge theories have provided us with a unique non-perturbative tool which has, for the first time, enabled us to attack the problem of the calculation of such fundamental quantities as the mass of the proton or the deconfinement temperature, starting from first prin- ciples. One of the outstanding problems in this field has been the proper in- clusion of the fermion determinant. More specifically, one is usually inter- ested in obtaining <Q> for a physical observable 8: <e> = Z-l j II dUi.e.e -SG(U) . det (D(U) + m) (1) XII! where Z = j II dU#.e -SG(U) XYiJ l det (D(U) + m) . Here D(U) + m, which is the inverse fermion propagator matrix, has a dimension 3N;NB. assuming the lattice to be of size Nz x Ng and that the staggered ferm- ions have been employed. Even for a modest 83 x 4 lattice thus the matrix is 6144 x 6144, and the Monte Carlo procedure would demand that its determinant be evaluated at least a few million times in order to obtain statistically signi- ficant results. Clever tricks are therefore necessary to include the determin- ant precisely, yet at a low computational cost. *) This work was supported by the U. S. Department of Energy under Contracts LIE-AC02-76CH00016 and DE-AT03-81-ER40029. **) Address after 1 November 1986, and permanent address: Theory Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India. 037559474/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)